Piano Accordions - with a piano style keyboard on the right hand and buttons on the left hand.
The number of bass buttons ususally relates to the number of treble keys, the table below shows typical combinations () denotes newer models which have managed to fit extra buttons into the casing.

Treble keys

bass buttons

treble Voices

26 or 30

24 / 32 / 48 / (72)

2 - 3

34

60 / 72 / (96)

3 - 4

37

80 / 96 / (120)

4 - 5

41 or 45

120

4 - 5

Chromatic Button accordion - with a keyboard consisting of rows of buttons arranged chromatically. There are two main systems B and C.

There can be 3 to 5 rows of horizontal treble buttons. In a 5 row chromatic, two additional rows repeat the first 2 rows to give options in fingering.

Diatonic Button accordion - or melodeon is a type of button accordion where the melody-side keyboard plays a different note in each direction . The bass side usually contains the principal chords of the instrument's key and the root notes of those chords.

The available notes on the melody side are based on different keys. For example, you could have a 1-row melodeon in the key of G. This would give you the notes G/A - B/C - D/E - F#/G spread over 4 buttons. Commonly used melodeons nowadays include the D/G box with 2 rows, used especially in English traditional music, while instruments in G/C, C/F or G/C/F (with three treble rows of buttons), are widely used in France, Italy and central/eastern Europe.
Irish traditional musicians generally favour instruments in B/C or C#/D.
There are many variations on these layouts, with 2½ row melodeons (a.k.a. "Club" system after the Hohner originals, accidentals and various options which players sometimes customize to suit their own requirements.
More information on melodeon's is available on this website http://info.melodeon.net

Stradella Bass System - is the standard layout on the bass side of most piano and chromatic accordions, it uses columns of buttons arranged in a circle of fifths; this places the principal major chords of a key (I, IV and V) in three adjacent columns. Each column contains, in order:
The major third above (or minor sixth below) the root ("counter-bass")
The root note
The major chord
The minor chord
The dominant seventh chord
The Diminished seventh chord
The following chart shows a standard 120-button Stradella layout.

Free Bass

Unlike the Stradella-bass system, all of the buttons on a free-bass keyboard play single notes. The free-bass also has a bigger range of notes than the Stradella system. Due to this, the free bass system is used more often to play serious classical music.

Convertor bass systems can switch between the Stradella and free-bass system, while some accordions have free-bass only or auxiliary free-bass rows in addition to the Stradella buttons (sometimes called a bassetti).

Parts of the accordion

The accordion consists of two wooden boxes joined by a bellows. These boxes house the reed blocks for the right and left hands. Each side has grilles in order to allow air in and out of the instrument, and to allow the sound to better project.

Bellows

The bellows is the most recognizable part of the accordion, they are made from pleated layers of cloth and cardboard with added leather and metal.
The frames of the bellows usually made of wood are glued to the bellow and fit inside the body of the accordion with a thin gasket between the frame and the body to create a seal, usually held in place by pins but sometimes screws.

ReedsThe reeds in an accordion are what actually generate the sound you hear, air passing across the reed tounge makes it vibrate generating a sound at a specific frequency.
The reed tongues (the part that vibrates) are riveted to a reed plate, two reeds per plate one on each side and there is a valve on the side opposite the reed to stop air passing the other way.

Reed BlocksThe reeds are attached to a wooden frame called a reed block, typically the reeds are held on with reed wax which is a mixture of beeswax, rosin and oil but they can also be pinned on leather.

Cassotto / Tone Chamber

A tone chamber is a cavity designed into the internal structure of some piano and chromatic accordions through which the sound from selected sets of reeds (normally Bassoon for single cassotto / bassoon and clarinet for double cassotto) must pass before reaching the listener.
The main purpose of the tone chamber is to give those reeds a more mellow sound.
It also makes some improvement in the response time of the lower notes.
These accordions will also typically have hand made reeds.

Pallet / Keyboard Mechanism

Pressing a key lifts a pallet letting the air flow across the reeds when you move the bellows, releasing the key a spring closes the pallet back down stopping the flow of air. Pallets can be made of wood, metal or plastic with a layer of felt and then a layer of leather which sits over the holes in the pallet board that lead to the reed blocks. In a cassotto accordion you have two pallets one for the reeds out of cassotto and one for the reeds in cassotto as you can see in the picture on the right.

Bass Mechanism
The bass mechanism of the accordion appears very complex but is simply alot of small levers, when you push a bass button (or counter bass) your rotating an arm which lifts a pallet on the bass pallet board, when you press a chord you open three pallets which correspond to the notes in the chord you are playing.

Couplers / Registers
The couplers on an accordion change the reed combinations that can play at the same time, they open slides between the pallet and the reed block either allowing air to pass through or blocking it.

Coupler Markings & Voices
Accordions can have up to 5 voices on the right hand, each voice is represented by a dot.

Piccolo (4')

Clarinet (8')

Bassoon (16')

Clarinet (8') tuned sharp

Clarinet (8') tuned flat

Master 3 voice

Musette 3 voice

Musette 4 voice

Double Octave 4 voice

5 voice

How many Reeds are in an accordionThe number of reeds in an accordion depends on the number of notes and number of voices, if you have a 41 note keyboard with four voices there are 41 notes X 4 voices X 2 reeds =
328 reeds in the treble.
In the bass end there are blocks of twelve reeds with up to five voices so 12 x 5 x 2 =120 reeds giving a total of 448 reeds in a standard full size accordion all of which have to be tuned for your accordion to sound the way it does.